Consider the following statements: 1. The general solution of d y d x =f(x)+x is of the form y=g(x)+c , where c is an arbitrary constant. 2. The degree of ( d y d x )^2=f(x) is 2 . Which of the above statements is/are correct?

Step-by-step solution

Statement 1: The general solution of d y d x =f(x)+x Now integrating on both side d y d x = [f(x)+x] d x y=f(x)+C Statement 1 is correct. Statement 2: d y d x =f(x)+c Squaring both sides, aligned & ( d y d x )^2=(f(x)+c)^2 & ( d y d x )^2= [f(x)^2+2 cf (x)+c^2 ] aligned Hence, the differential equation is of order -1 and degree -2 . both Statements 1 and 2 are correct. Option (C) is correct.